Introduction to Functional Programming

... lambda calculus. It is widely agreed that languages such as Haskell and Miranda are purely functional, while SML and Scheme are not. However, there are some small differences of opinion about the precise technical motivation for this distinction. Scheme and Standard ML are predominantly functional ...

... lambda calculus. It is widely agreed that languages such as Haskell and Miranda are purely functional, while SML and Scheme are not. However, there are some small differences of opinion about the precise technical motivation for this distinction. Scheme and Standard ML are predominantly functional ...

Recursion 2

... be easier to write and understand - e.g. Towers of Hanoi. However, avoid using excessively recursive algorithms even if the code is simple. ...

... be easier to write and understand - e.g. Towers of Hanoi. However, avoid using excessively recursive algorithms even if the code is simple. ...

Intro to Theano

... This isn’t available in older versions of python, and will limit the portability of your code ...

... This isn’t available in older versions of python, and will limit the portability of your code ...

Functional Programming in CLEAN

... descriptions of the way a result can be computed, given some arguments. A natural way to write a computer program is therefore to define some functions and applying them to concrete values. We need not to constrain ourselves to numeric functions. Functions can also be defined that have, e.g., sequen ...

... descriptions of the way a result can be computed, given some arguments. A natural way to write a computer program is therefore to define some functions and applying them to concrete values. We need not to constrain ourselves to numeric functions. Functions can also be defined that have, e.g., sequen ...

Lazy evaluation - Computer Science and Engineering

... • Functional languages can be eager, lazy or a mix of the two. • Functional language SML uses eager evaluation whereas languages like Haskell and Miranda use lazy evaluation scheme. • In lazy languages, function arguments may be infinite data structures (especially lists), the components of which a ...

... • Functional languages can be eager, lazy or a mix of the two. • Functional language SML uses eager evaluation whereas languages like Haskell and Miranda use lazy evaluation scheme. • In lazy languages, function arguments may be infinite data structures (especially lists), the components of which a ...

Semantics Directed Program Execution Monitoring

... deﬁned in the “standard algebras” section in Appendix A). There are two unconventional features in this interpreter: First is the explicit use of the fixpoint of functionals to specify the valuation functions (see lazyEvalf); this will allow us later to derive enhanced valuation functions that “inhe ...

... deﬁned in the “standard algebras” section in Appendix A). There are two unconventional features in this interpreter: First is the explicit use of the fixpoint of functionals to specify the valuation functions (see lazyEvalf); this will allow us later to derive enhanced valuation functions that “inhe ...

Calculating Functional Programs - Research School of Computer

... norm rather than the exception. There is clearly a need for more reliable methods of program construction than the traditional ad hoc methods in use today. What is needed is a science of programming, instead of today’s craft (or perhaps black art). As Jeremy Gunawardena points out [15], computation ...

... norm rather than the exception. There is clearly a need for more reliable methods of program construction than the traditional ad hoc methods in use today. What is needed is a science of programming, instead of today’s craft (or perhaps black art). As Jeremy Gunawardena points out [15], computation ...

Coding a Lisp Interpreter in Shen: a Case Study

... comparable to the vague intuitive notion of computability that existed prior to Turing's [23] definition of computability in 1936. We cannot prove formally that Turing's account of computability meets our intuitive concept because formal proof begins only when our intuitions have been given shape. H ...

... comparable to the vague intuitive notion of computability that existed prior to Turing's [23] definition of computability in 1936. We cannot prove formally that Turing's account of computability meets our intuitive concept because formal proof begins only when our intuitions have been given shape. H ...

Interpreters for two simple languages – including exercises

... Every top-level declarations let id = e is subject to the following restriction on e: • All monomorphic expressions are OK, • all value expressions are OK, even polymorphic ones, and • at top-level, polymorphic non-value expressions are forbidden An expresssion e in a declaration of the form let mut ...

... Every top-level declarations let id = e is subject to the following restriction on e: • All monomorphic expressions are OK, • all value expressions are OK, even polymorphic ones, and • at top-level, polymorphic non-value expressions are forbidden An expresssion e in a declaration of the form let mut ...

Q-Midi - Q - Equational Programming Language

... expression is evaluated in a symbolic fashion by repeatedly applying equations. The resulting expression, to which no more equations are applicable, is said to be in “normal form” and constitutes a “value” in the Q language. Despite its conceptual minimalism, Q is not a toy language. First, term rew ...

... expression is evaluated in a symbolic fashion by repeatedly applying equations. The resulting expression, to which no more equations are applicable, is said to be in “normal form” and constitutes a “value” in the Q language. Despite its conceptual minimalism, Q is not a toy language. First, term rew ...

View raw file - aaa

... Not simple to manipulate. λ x . (λ y . x) x = λ . (λ . 2). 1 Need to shift indices in substitution to avoid ...

... Not simple to manipulate. λ x . (λ y . x) x = λ . (λ . 2). 1 Need to shift indices in substitution to avoid ...

Declarative Programming in Escher

... Indeed, Escher goes well beyond Godel in its ability to allow function denitions, its higher-order facilities, its improved handling of sets, and its declarative input/output. Escher also goes well beyond Haskell in its ability to run partly-instantiated predicate calls, a familiar feature of logi ...

... Indeed, Escher goes well beyond Godel in its ability to allow function denitions, its higher-order facilities, its improved handling of sets, and its declarative input/output. Escher also goes well beyond Haskell in its ability to run partly-instantiated predicate calls, a familiar feature of logi ...

COS220lec52_FP

... Introduction to FP Imperative programming vs. functional programming Language applied to functional programming is LISP – LISt Programming. It was invented to provide language features for list processing, the need for which grew out of the first application in the area of AI, expert systems, knowl ...

... Introduction to FP Imperative programming vs. functional programming Language applied to functional programming is LISP – LISt Programming. It was invented to provide language features for list processing, the need for which grew out of the first application in the area of AI, expert systems, knowl ...

nil

... be transformed into an iteration. Tail call optimization: » If the function is tail recursive, the result of the last call can be returned directly to the original caller. » This decreases the amount of stack space used and improves efficiency. ...

... be transformed into an iteration. Tail call optimization: » If the function is tail recursive, the result of the last call can be returned directly to the original caller. » This decreases the amount of stack space used and improves efficiency. ...

User`s Functions in Standard Prolog

... A data term represents itself. No evaluation is done to data terms. Constants (atoms and numbers), variables, and subterms introduced (after compilation4 ) by variable instantiation are always data terms. This later means that an evaluation step “is only performed at a (compound) subterm which is no ...

... A data term represents itself. No evaluation is done to data terms. Constants (atoms and numbers), variables, and subterms introduced (after compilation4 ) by variable instantiation are always data terms. This later means that an evaluation step “is only performed at a (compound) subterm which is no ...

The Continuity of Monadic Stream Functions

... two components c = hcS , cP i with cs : X → S and cP : (x : X) → (P s) → X. The commutativity of the diagram can then be expressed by the two equations shape (ĉ x) = cS x subs (ĉ x) p = ĉ (cP x p). ...

... two components c = hcS , cP i with cs : X → S and cP : (x : X) → (P s) → X. The commutativity of the diagram can then be expressed by the two equations shape (ĉ x) = cS x subs (ĉ x) p = ĉ (cP x p). ...

Closure and Environment

... Nested HOL is a key feature in modern functional programming languages And now has grown into other language ...

... Nested HOL is a key feature in modern functional programming languages And now has grown into other language ...

Lecture Notes

... A set can have another set as one of its elements. For example, the set A = {{a, b, c}, d} contains two elements {a, b, c} and d; and the first element is itself a set. We will use the notation x ∈ S to denote that x is an element of (“belongs to”) the set S. A set A is a subset of another set B, de ...

... A set can have another set as one of its elements. For example, the set A = {{a, b, c}, d} contains two elements {a, b, c} and d; and the first element is itself a set. We will use the notation x ∈ S to denote that x is an element of (“belongs to”) the set S. A set A is a subset of another set B, de ...

Types and Programming Languages

... of fix expressions. There’s a small issue: let allows us to define values as well as functions, but we don’t want to allow recursively-defined values (why not?) A convenient solution is to distinguish between value and function definitions by using the keywords val and fun. let fun f(x:int):int = bo ...

... of fix expressions. There’s a small issue: let allows us to define values as well as functions, but we don’t want to allow recursively-defined values (why not?) A convenient solution is to distinguish between value and function definitions by using the keywords val and fun. let fun f(x:int):int = bo ...

Programming with Miranda

... assignment statement—a functional programmer does not assign values to storage locations, but instead has the ability to give names to the values of expressions; these names may then be used in other expressions or passed as parameters to functions. 2. The fact that in a functional language a name o ...

... assignment statement—a functional programmer does not assign values to storage locations, but instead has the ability to give names to the values of expressions; these names may then be used in other expressions or passed as parameters to functions. 2. The fact that in a functional language a name o ...

Imperative languages

... Operations with variables • Program must allocate the memory space before the variable is used • The allocation can be either static or dynamic • Program reads the contents of the memory in the moment we refer to the identifier (name) • The contents of the memory referred by a variable is changed b ...

... Operations with variables • Program must allocate the memory space before the variable is used • The allocation can be either static or dynamic • Program reads the contents of the memory in the moment we refer to the identifier (name) • The contents of the memory referred by a variable is changed b ...

Imperative languages

... Operations with variables • Program must allocate the memory space before the variable is used • The allocation can be either static or dynamic • Program read the contents of the memory in the moment we refer to the identifier (name) • The contents of the memory referred by a variable is changed by ...

... Operations with variables • Program must allocate the memory space before the variable is used • The allocation can be either static or dynamic • Program read the contents of the memory in the moment we refer to the identifier (name) • The contents of the memory referred by a variable is changed by ...

Programming Language Theory and its Implementation

... The -calculus is a theory of higher-order functions, i.e. functions that take functions as arguments or return functions as results. It has inspired the design of functional programming languages including LISP 53], ML 55], Miranda 70] and Ponder 17]. These languages provide notations for denin ...

... The -calculus is a theory of higher-order functions, i.e. functions that take functions as arguments or return functions as results. It has inspired the design of functional programming languages including LISP 53], ML 55], Miranda 70] and Ponder 17]. These languages provide notations for denin ...

Functional Programming in Haskell

... • Values don't change over program execution: contrast x=x+1 etc. of Java, C, … •… instead we describe relations between values by means of (fixed) functions. ...

... • Values don't change over program execution: contrast x=x+1 etc. of Java, C, … •… instead we describe relations between values by means of (fixed) functions. ...

... • Values don't change over program execution: contrast x=x+1 etc. of Java, C, … •… instead we describe relations between values by means of (fixed) functions. ...